Photochemistry_of_Organic

product that preserves one or more of the symmetry elements along the reaction coordinate. We can then connect states of the reactant and the product that belong to the same irreducible representation. We begin by estimating the energies of the lowest electronic states of the reactant and of the possible product(s). This information may be drawn from electronic spectra, calculations or educated guesswork. To be sure, the preferred reaction path may well be one not retaining any symmetry. We choose a symmetrical reaction path only because it allows us to construct a correlation diagram. Because potential energy surfaces are continuous, this path will give some indication of the shape of the surfaces nearby. Consider the protonation of a ketone in its lowest n,p excited triplet state (Figure 4.32). The carbonyl moiety is planar and we assume that the proton attacks the carbonyl oxygen in the plane of symmetry.

Figure 4.32 State-symmetry diagram for the protonation of an n,p excited triplet ketone

The n,p state of the ketone is strongly destabilized by protonation of the oxygen atom, so that it will have a higher energy than the p,p state in the conjugate acid. We can now classify the two lowest excited singlet states of reactant and product by simply counting the unpaired electrons. The wavefunctions of the closed-shell ground state and also those of the p,p excited states are symmetric (s), because they contain an even number of electrons in the antisymmetric (a) p and p orbitals (recall that a a ¼ s, Section 4.4). Those of the n,p states are antisymmetric (a) with respect to the plane of symmetry, because they have a singly occupied p -orbital and the n-orbital is symmetric, a s ¼ a. Connecting the states of the same symmetry, we see that the protonation of an n,p excited ketone is a state-symmetry forbidden reaction, as long as the plane of symmetry is retained.

Benzophenone is a very weak base in the ground state and its protonation requires very strong acid. The acidity of the conjugate acid, pKa(S0) ¼ 4.7, is, however reduced by four orders of magnitude in the excited triplet state pKa(S1) ¼ 0.4 (see also Case Study 5.1). Nevertheless, the protonation of triplet benzophenone is much slower than usual for an oxygen-protonation reaction, kHþ ¼ 3.8 108 M 1 s 1, and it is the rate-determining step preceding the faster hydration of the aromatic nucleus, k0 ¼ 1.5 109 s 1 (Scheme 4.4).332 The hydrated intermediate regenerates benzophenone after ISC and is responsible for the quenching of aromatic ketones by protons in aqueous acid reducing the quantum yields of their usual reactions. It does, however, open the way to some novel

Scheme 4.4 Photohydration of benzophenone in aqueous acid

photoreactions333Ð335 of substituted aromatic ketones in aqueous acid (see also Scheme 6.239). The in-plane protonation of phenylnitrene is also state-symmetry forbidden (see Section 5.4.2).

A state-symmetry diagram for the Norrish type II reaction (Section 6.3.4) shows that it is allowed only from the n,p singlet and triplet states to give the covalent biradicals (Section 5.4.4) 1Ds;p and 3Ds;p, respectively, but not from p,p states (Figure 4.33).331

Figure 4.33 State-symmetry diagram for intramolecular hydrogen abstraction. The symmetry labels refer to the plane of the carbon chain

The orbital correlation diagrams put forth by Woodward and Hoffmann336 for electrocyclic and sigmatropic reactions (Section 6.1.2) and for cycloaddition reactions (Section 6.1.5) are well known and the details of their construction are not reiterated here. We show only the case of the [2s þ 2s] cycloaddition of two ethene molecules to cyclobutane as an example (Figure 4.34).

Figure 4.34 Woodward–Hoffmann MO correlation diagram for [2 þ 2] cycloaddition. The labels s (symmetric) and a (antisymmetric) refer to the symmetry planes sxz and syz in that order

To predict the shape of potential energy surfaces along the symmetry-retaining reaction coordinate from an MO correlation diagram, one must construct a correlation diagram of the electronic conÞgurations (Figure 4.35).

Figure 4.35 Correlation diagram of the lowest configurations in [2 þ 2] cycloaddition

It is seen that the ground conÞguration of the two ethene molecules correlates with a doubly excited conÞguration of cyclobutane because the electron pair in the antisymmetric combination of the bonding p-orbitals of the ethenes (symmetry sa) is lifted to the antibonding s orbital of the same symmetry in cyclobutane. Starting from the singly excited conÞguration xsa ! as of symmetry aa, one ends up in the singly exited conÞguration

11.Why do cross-conjugated alkenes absorb at shorter wavelengths than linearly conjugated alkenes? Compare hexa-1,3,5-triene and 1,1-divinylethene. [PMO]

4.11 Appendix

4.11.1First-Order Perturbation

Assume that the solution for the H€uckel secular determinant of a parent molecule has been determined, that is, that the eigenvalues «j and the associated set of orthonormal HMOs cj are known. We now introduce a ÔsmallÕ perturbation of the system, say by adding a substituent or by replacing one of the C atoms by a heteroatom, for example N. To this end, we must Þrst express the MO energies «j as a function of the MO coefÞcients. Inserting

Equation 4.38

The right-hand expression results from replacing the integral over sums by sums of

integrals. We replace the integrals < mj^ j n> by the parameter list (Equation 4.3), f

f H

retaining the atomic indices that assign the parameters to speciÞc atoms or bonds, because we will introduce perturbations at some particular atoms, am ¼ a þ dam, or bonds, bmn ¼ b þ dbmn:

n6¼m

Equation 4.39

The last sum in Equation 4.39 runs only over pairs of atoms that are bound (m n),

because mn ¼ < mj^ j n> is zero otherwise, and is multiplied by two, because each bond b f H f

appears twice in the double sum on the left and bmn ¼ bnm. Introducing a perturbation at atom m, am ¼ a þ dam, the energy «j will change by d«j ¼ (q«j/dam)dam. The partial derivative of Equation 4.39 is (q«j/dam) ¼ cjm2, so that we obtain Equation 4.13 for the effect of an inductive perturbation dam on «j. Similarly, a change in the resonance integral between atoms m and n, dbmn, will change the energy «j by d«j ¼ (q«j/dbmn)dbmn. The partial derivative of Equation 4.39 with respect to bmn is (q«j/dbmn) ¼ 2cjmcjn (Equation 4.14).

operator of the parent molecule and ^ the perturbation operator. We could, of course, set up h

already have a good starting point for the new system. Therefore, the wavefunctions are set up as linear combinations of the functions cðj 0Þ (Equation 4.40).

We have assumed that «i(0) is not degenerate with any other eigenvalue «i(0) so that only the Þrst bracket can vanish and it will do so if

Equation 4.44

where the sum represents the second-order perturbation d«ð12Þ. The same can be done for any row i of Equation 4.42 to give the general equation for second-order perturbation (Equation 4.15), in which the upper indices (0) marking the eigenvalues «i of the unperturbed system have been dropped.

5

Photochemical Reaction Mechanisms

and Reaction Intermediates

5.1 What is a Reaction Mechanism?

The term reaction mechanism is part of the everyday language of chemists, yet it conveys different things to different people. The IUPAC Gold book (www.goldbook.iupac.org) defines the mechanism of a reaction as A detailed description of the process leading from the reactants to the products of a reaction, including a characterization as complete as possible of the composition, structure, energy and other properties of reaction intermediates, products and transition states. An acceptable mechanism of a specified reaction (and there may be a number of such alternative mechanisms not excluded by the evidence) must be consistent with the reaction stoichiometry, the rate law and with all other available experimental data, such as the stereochemical course of the reaction. On the basis of Occam s razor (Section 3.7.4), one should always choose the simplest mechanism that is consistent with all available evidence.

A truly mechanistic (in the sense of classical mechanics) description of a molecule s reaction is in fact prohibited by Heisenberg s uncertainty relations (Equation 2.1). Some reaction mechanisms of small molecules in the gas phase have been elucidated in the utmost detail, that is, reaction rate constants have been determined for individual rotational and vibrational quantum states of the reactant. We take a more modest view: a reaction mechanism is the step-by-step sequence of elementary processes and reaction intermediates by which overall chemical change occurs.

The mechanism of a photoreaction should ideally include a detailed characterization of the primary events as outlined by the classification of photochemical reaction pathways in Section 2.3; the lifetimes of the excited states that are involved in the reaction path, the quantum yields and hence the rate constants of all relevant photophysical and photochemical processes, in addition to the information about the structure and fate of any reactive intermediates, their lifetimes and reactivities.

Photochemistry of Organic Compounds: From Concepts to Practice Petr Klán and Jakob Wirz © 2009 P. Klán and J. Wirz. ISBN: 978-1-405-19088-6

The Gibbs free energy of photoinduced electron transfer, DetG , in an excited encounter complex (D A) can be estimated from Equation 5.1, where E (D. þ /D) is the standard electrode potential of the donor radical cation, E (A/A. ) that of the acceptor A and DE0–0 is the 0–00 excitation energy of the excited molecule (D or A ) that participates in the reaction.

DetG ¼ NAfe½E ðD. þ=DÞ E ðA=A. Þ& þ wðD. þ ; A. Þ wðD; AÞg DE0 0

Equation 5.1 Free energy of photoinduced electron transfer

In the general case, the electrostatic work terms w that account for the Coulombic attraction of reactants (D, A) and products (D þ , A ) are w(D, A) ¼ zDzAe2/(4p«0«ra) and w(D þ , A ) ¼ zD þ zA e2/(4p«0«ra), where zD and zA are the charge numbers of donor D and acceptor A prior to electron transfer and zD þ and zA are those after electron transfer. For neutral species D and A, zD ¼ zA ¼ 0. Choosing convenient units and collecting the constants we obtain the scaled Equation 5.2.

Equation 5.2 Scaled equation for the free energy of electron transfer

Mixing electron donor and acceptor molecules in apolar solution may be accompanied by the formation of weakly associated charge-transfer or electron-donor–acceptor(EDA) complexes in the ground state.342 In a simple quantum mechanical treatment, the groundstate wavefunction of EDA complexes may be described as a resonance hybrid of a no-bond ground state (A D) and a charge-transfer state (A D þ ) (Equation 5.3), where

c0,no bond 1 and c0,dative 0.

C0 ¼ c0;no bondCðA DÞ þ c0;dativeCðA D þ Þ

Equation 5.3 Wavefunction of an EDA ground state complex

The charge-transfer excited state is then represented by Equation 5.4, with c1,no bond 0

and c1,dative 1.

C1 ¼ c1;no bondCðA DÞ þ c1;dativeCðA D þ Þ

Equation 5.4 Wavefunction of an excited charge-transfer state

These wavefunctions account for the attractive force between A and D leading to the formation of an EDA complex, for its increased polar character and also for the existence of charge-transfer absorption that is often observed when EDA complexes form. Lowlying excited states of A or D þ must be included in the wave function to describe additional charge-transfer bands. These bands appear in addition to the absorption bands of the molecules A and D; they are usually broad and of low oscillator strengths because there is little overlap between the HOMO of the donor and the LUMO of the acceptor (Section 4.4, Equation 4.20). Many examples of the formation of EDA complexes between, for example, tetracyanoethylene and aromatic hydrocarbons are known. The